If the packet data indicator on the device display becomes active even though there is no application connecting to internet, the device may be trying to retrieve a multimedia message from the multimedia message centre. To stop the device from making a data connection, select Menu > Messaging > Options > Settings > Multimedia message > Multimedia retrieval. Select Manual to have the multimedia messaging centre save messages to be retrieved later, or Off to ignore all incoming multimedia messages. If you select Manual, you receive a notification when you have a new message in the multimedia message centre. If you select Off, the device does not make any network connections related to multimedia messaging.
If the packet data indicator is constantly active, check if the packet data connection is configured to be constantly on. To set the device to activate a packet data connection only if you start an application or action that needs it,select Menu > Settings > Connectivity > Admin.settings> Packet data > Packet data connection > When needed. If you select When available and you are in a network that supports packet data, the device registers to the packet data network always when the network is available. Starting an active packet data connection (for example, to send and receive e-mail) is then quicker than if the device establishes a packet data connection when needed.
If the above settings don't help, switch the device off and then on again.
Note that there can also be an application in your device that automatically connects to internet, e.g. the home screen widgets or email client. If you don't want the connection to be automatically established, change the connection settings for the applications (e.g. disable automatic synchronisation in email client and select Options > Widgets to offlinemode in home screen).